In consideration of Orbital Angular Momentum (OAM) potentialities of increasing transmission capacity and since RF spectrum shortage problem is deeply felt in radio communications sector, recently a lot of experimental studies have been carried out on the use of OAM states, or modes, at RF (also known as radio vortices) in order to try to enhance RF spectrum reuse.
In this connection, reference may, for example, be made to:                Mohammadi S. M. et al., “Orbital Angular Momentum in Radio—A System Study”, IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, IEEE SERVICE CENTER, PISCATAWAY, N.J., US, vol. 58, no. 2, 1 Feb. 2010, pages 565-572, which shows that standard antennas arranged in circular arrays can be used to generate RF beams carrying OAM;        
Tamburini F. et al., “Encoding many channels in the same frequency through radio Vorticity: first experimental test”, arXiv.org, 12 Jul. 2011, Ithaca, N.Y., USA, which experimentally shows that it is possible to propagate and use the properties of twisted non-monochromatic incoherent radio waves to simultaneously transmit several radio channels on one and the same frequency by encoding them in different (and, thence, orthogonal) OAM states (even without using polarization or dense coding techniques);                GB 2 410 130 A, which discloses a planar phased array antenna for transmitting and receiving OAM radio vortex modes, which antenna comprises a circular array of cavity backed axial mode spiral antenna elements whose phase is controlled such that the phase of each antenna element changes sequentially about the array; and        WO 2012/084039 A1, which discloses a transmit antenna arrangement comprising N antenna elements arranged along a circumference with an angular separation of α degrees between neighboring antenna elements, the antenna arrangement comprising an OAM encoder arranged to receive N input signals for transmission, indexed from M=−(N−1)/2 up to M=(N−1)/2 for odd N and from M=−(N−2)/2 up to N/2 for even N; the OAM encoder connecting each input signal to each antenna element and giving each input signal M at each antenna element a phase shift of M*α relative to the phase of the same input signal M at an adjacent antenna element; wherein two or more antenna elements are directional, have their directivity in the same direction, and have an antenna aperture higher than, or equal to, 5λ, where λ is the wavelength of the N input signals.        
From a mathematical perspective, the transmission of an OAM mode (or state) at a single RF (i.e., by using a pure tone) implies that the electrical field on the radiating aperture can be represented as:F=(ρ,φ)=F(ρ)ekkφ,where ρ and φ are the cylindrical coordinates on the radiating aperture, j is the imaginary unit, and k is a positive or negative integer.
The radiated field can be represented in the far zone as:
            E      ⁡              (                  ϑ          ,          φ                )              =                  1        R            ⁢                        ∫          ∫                S            ⁢              F        ⁡                  (                      ρ            ,            ϕ                    )                    ⁢              ⅇ                              -            j                    ⁢                                          ⁢          2          ⁢          π          ⁢                      ρ            λ                    ⁢                      sin            ⁡                          (              ϑ              )                                ⁢                      cos            ⁡                          (                              φ                -                ϕ                            )                                          ⁢      ρ      ⁢              ⅆ        ρ            ⁢              ⅆ        ϕ              ,
where ν and φ are the spherical coordinates in the far field, R denotes the radius of the sphere centered on the radiating aperture, S denotes the integration surface used at reception side, and λ denotes the wavelength used.
As is known, due to intrinsic characteristics of OAM, an OAM mode transmitted at a single RF (i.e., by using a pure tone) is affected by a phase singularity which creates a null at the bore-sight direction, thereby resulting thatE(0,0)=0.
In order for said phase singularity to be compensated, the integration surface S used at reception side should be sized so as to include the crown peak generated by the OAM mode.
In particular, the integration surface S used at reception side should be different for each OAM mode and, considering the sampling theorem applied to the radiating antenna, should have an area given by:
            Δ      ⁢                          ⁢      S        =                  ΔΩ        ⁢                                  ⁢                  R          2                    =              2        ⁢                              (                                          λ                D                            ⁢              R                        )                    2                      ,where D denotes the diameter of the radiating antenna.
Therefore, the price to be paid with pure OAM modes transmitted by using pure tones (i.e., single radiofrequencies) is that the dimensions of the equivalent receiving antenna depend on the distance R from, and on the diameter D of, the transmitting antenna.
This solution is impractical for satellite communications, where the aperture efficiency and the size of the antennas are very critical issues. For example, in geostationary-satellite-based communications in Ka band, for a ground antenna having a diameter D of about 9 m, the diameter of the receiving ring on board the geostationary satellite should be of the order of 50 Km, thereby resulting impractical.
Thence, in view of the foregoing, the main criticality in using radio vorticity in practical systems is that the orthogonality between OAM modes depends on the size of antennas, on the distance between the transmitting and receiving antennas, and on the need for the receiving antenna to operate as an interferometer basis (as, for example, disclosed in the aforesaid papers “Orbital Angular Momentum in Radio—A System Study” and “Encoding many channels in the same frequency through radio Vorticity: first experimental test”, in GB 2 410 130 A and in WO 2012/084039 A1). These constraints result in OAM-based radio communication systems which are inefficient and unusable for very long distances, such as the ones involved in satellite communications.
Moreover, further criticalities in the use of radio vorticity for satellite communications are represented by the need of an extremely accurate mutual pointing of the transmitting and receiving antennas, and by the unfeasibility of the geometry for Earth-satellite configurations due to the criticality of the positioning of the receiving antennas (or the receiving antenna elements).
A solution to the aforesaid technical problems is provided in the International Application No. PCT/IB2012/056804 (whose content is herewith enclosed by reference) filed on 28 Nov. 2012 in the name of EUTELSAT S. A., published on 30 Jan. 2014 with publication number WO 2014/016655 A1, and concerning a multidimensional space modulation technique for transmitting and/or receiving radio vortices at frequencies ranging from a few KHz to hundreds of GHz. Specifically, the multidimensional space modulation technique according to WO 2014/016655 A1 allows to transmit and/or receive orthogonal RF OAM modes in one and the same direction (i.e., the bore-sight direction) and to overcome, at the same time, the aforesaid technical problems caused by OAM phase singularity at the bore-sight direction, thereby allowing the use of radio vortices also for long-distance radio communications, such as satellite communications.
In particular, the multidimensional space modulation according to WO 2014/016655 A1 is actually a phase modulation applied to signals to be transmitted at RF such that to result in orthogonal radio vortices along the bore-sight direction. Therefore, the modulation according to WO 2014/016655 A1 is called multidimensional space modulation because it allows orthogonal RF OAM modes to be transmitted and/or received in one and the same direction, namely the bore-sight direction, wherein each OAM mode represents a specific space channel along the bore-sight direction, which specific space channel is orthogonal to all the other space channels represented by the other OAM modes.
In order for the multidimensional space modulation according to WO 2014/016655 A1 to be better understood, attention is drawn, by way of example, to the fact that, as is known, a twisted RF signal having, or carrying, the OAM mode m=+1 (where m, as is known, is called topological charge) is characterized by only one clockwise rotation of 360° of the Poynting vector around the propagation axis per period T and, thence, it can be generated by transmitting, for example by means of four ring-arranged transmitting antenna elements, RF signals associated with phases of 0°, 90°, 180°, and 270° clockwise distributed among said four ring-arranged transmitting antenna elements. Instead, WO 2014/016655 A1 proves that it is possible and convenient, in order to transmit at RF the OAM mode m=+1 and, at the same time, to solve the problem caused by OAM phase singularity at the bore-sight direction, to exploit only one antenna transmitting the four different phases 0°, 90°, 180°, and 270° at different times (or at different frequencies) with a time step of T=T/4. This possibility increases the efficiency of the transmitting and receiving configuration, which can work regardless of the elementary antenna element spacing in an antenna array.
From a conceptual perspective, according to WO 2014/016655 A1, in order to manage OAM rotation, namely in order to control the speed of rotation of an RF OAM mode about the bore-sight direction, a supplementary phase modulation is introduced, which leaves only a residue of the OAM twist and keeps the OAM signature in a limited bandwidth. This residual rotation achieved by means of the supplementary phase modulation allows a signal having a proper bandwidth to be orthogonal to another signal having a different rotation (multiple of the minimum one). Therefore, an RF twisted wave can be transmitted by means of a modulated waveform and can be received by an antenna operating in the complex conjugate mode. The received signal is equal to the transmitted one, apart from standard attenuation and transmission and reception gains in a time period Tmod. The bandwidth increase does not prevent the transmission of plane waves (i.e., the OAM mode m=0), but limits the number of OAM modes at different central frequencies in the available bandwidth. The multidimensional space modulation according to WO 2014/016655 A1 allows to use a standard antenna in place of a phased array antenna, since the used signals are native orthogonal.
It is important to underline the fact that the generation of RF OAM modes by means of the multidimensional space modulation according to WO 2014/016655 A1 allows to drastically simplify the antenna design. In fact, the antenna does not need to take memory at the period of the carrier frequency of the phase between elements f0=1/T0. This duty is performed by the sampling frequency of the twisted waves, which is higher than the signal bandwidth; therefore the phase shift assigned to the sampling is already orthogonal in time; it follows that the antenna can be a standard one without the need of using a phased array configuration on either the antenna aperture, or, in case of a reflector antenna, the focal plane. Therefore, the multidimensional space modulation according to WO 2014/016655 A1 can be exploited in satellite communications by using already existing satellite and ground antennas.
In order for the multidimensional space modulation according to WO 2014/016655 A1 to be better understood, reference is made to FIG. 1, which shows a functional block diagram of a transmitting system (denoted as whole by 1), which is disclosed in WO 2014/016655 A1 and which exploits the aforesaid multidimensional space modulation for transmitting radio vortices at frequencies ranging from a few KHz to hundreds of GHz.
In particular, the transmitting system 1 comprises:                a signal generation section 10 designed to generate                    a first digital signal s0(t) carrying an information stream, having a given sampling period T0 and occupying a given frequency bandwidth W centered on a predefined frequency f0, and            up to 2N second digital signals sm(t), with —N≦m≦+N and N≧1 (for the sake of illustration simplicity in FIG. 1 only signals s+1(t), s−1(t), s+N(t) and s−N(t) are shown), each carrying a respective information stream, having a respective sampling period Tm=4|m|T0 (or Tm=3|m|T0) and occupying a respective frequency bandwidth W/4|m| (or W/3|m|) centered on said predefined frequency f0 (which can, conveniently, be an Intermediate Frequency (IF) thereby resulting that the first and second digital signals are IF digital signals);                        a device 100 for generating OAM modes, which is coupled with said signal generation section 10 to receive the first and second digital signals generated by the latter, and which is designed to                    apply, to each second digital signal sm(t) received from the signal generation section 10, a respective space modulation associated with a respective OAM mode m so as to generate a corresponding modulated digital signal carrying said respective OAM mode m, having the given sampling period T0, and occupying the given frequency bandwidth W, and            provide an output digital signal sout(t) based on the modulated digital signals and on the first digital signal s0(t) received from the signal generation section 10; and                        an RF transmission section 1000, which is coupled with the device 100 to receive therefrom the output digital signal sout(t), and which is designed to transmit at predefined radio frequencies the output digital signal sout(t) by means of a single antenna (which is not shown in FIG. 1 for the sake of illustration simplicity and which can be also a reflector antenna with a single feed) or an antenna array (which is not shown in FIG. 1 for the sake of illustration simplicity and which can be also a multi-feed reflector antenna), thereby transmitting an overall RF signal carrying                    said first digital signal s0(t) by means of a plane wave, and            said second digital signals sm(t), each by means of a corresponding radio vortex having the respective OAM mode m.                        
The aforesaid predefined radio frequencies can conveniently range from a few KHz to hundreds of GHz depending on the specific application for which the overall transmitting system 1 is designed.
Conveniently, the signal generation section 10 can be a signal generation section of a transmitting system for satellite communications (such as a transmitting system of a feeder link Earth station, of a satellite, or of a ground apparatus for satellite communications), or of a device for wireless communications, such as LTE-based communications.
Accordingly, the RF transmission section 1000 can conveniently be an RF transmission section of a transmitting system for satellite communications (such as a transmitting system of a feeder link Earth station, of a satellite, or of a ground apparatus for satellite communications), or of a device for wireless communications, such as LTE-based communications.
Additionally, FIG. 2 shows in greater detail the device 100 for generating OAM modes, which device 100 comprises 2N OAM mode generation modules. In particular, FIG. 2 shows, for the sake of illustration simplicity, only:
an OAM mode generation module 110 for generating OAM mode m=+1;
an OAM mode generation module 120 for generating OAM mode m=−1;
an OAM mode generation module 130 for generating OAM mode m=+N; and
an OAM mode generation module 140 for generating OAM mode m=−N.
In detail, a generic OAM mode generation module for generating OAM mode m is operable to apply to a respective second digital signal sm(t) received from the signal generation section 10 a respective space modulation associated with said OAM mode m so as to generate a corresponding space-modulated digital signal smsm(t) carrying said OAM mode m, having the given sampling period T0, and occupying the whole given frequency bandwidth W centered on said predefined frequency f0.
More in detail, the generic OAM mode generation module for generating the OAM mode m is operable to:                receive a synchronization signal synchm (not shown in FIG. 2 for the sake of illustration clarity) indicating the given sampling period T0 and, conveniently, also the sampling period Tm of the respective second digital signal sm(t) received from the signal generation section 10; and        apply the respective space modulation to said respective digital signal sm(t) by                    digitally interpolating said respective second digital signal sm(t) on the basis of the received synchronization signal synchm so as to generate a corresponding digitally-interpolated signal having the given sampling period T0;            applying to the digitally-interpolated signal a respective digital phase modulation associated with said OAM mode m such that to generate a corresponding phase-modulated signal carrying said OAM mode m with a predefined OAM mode rotation speed; and            digitally filtering the phase-modulated signal thereby obtaining a filtered signal which represents the aforesaid space-modulated digital signal smsm(t).                        
For example, the OAM mode generation module 110 is conveniently configured to:                receive, from the signal generation section 10, the second digital signal s+1(t) and a synchronization signal synch+1 indicating the given sampling period T0 and, conveniently, also the sampling period T+1=4T0 (or T+1=3T0) of the second digital signal s+1(t);        digitally interpolate the second digital signal s+1(t) by outputting, for each digital sample of said second digital signal s+1(t), four corresponding digital samples with time step (i.e., time distance) T0, thereby generating a corresponding digitally-interpolated signal having the given sampling period T0;        apply, to each set of four digital samples obtained by means of the digital interpolation, digital phase shifts related to the OAM mode +1 with the predefined OAM mode rotation speed (namely, digital phase shifts related to phase values 0, π/2, π and 3π/2) so as to generate a corresponding set of four phase-shifted digital samples, which corresponding set of four phase-shifted digital samples carries said OAM mode +1 with the predefined OAM mode rotation speed;        digitally filter each set of four phase-shifted digital samples obtained by means of the digital phase shifting so as to output a corresponding set of four filtered digital samples; and        combine the sets of four filtered digital samples obtained by means of the digital filtering into a single filtered signal which represents the space-modulated digital signal sms+1(t).        
Accordingly, the OAM mode generation module 120 is conveniently configured to:                receive, from the signal generation section 10, the second digital signal s−1(t) and a synchronization signal synch−1 indicating the given sampling period T0 and, conveniently, also the sampling period T−1=4T0 (or T−1=3T0) of the second digital signal s−1(t);        digitally interpolate the second digital signal s−1(t) by outputting, for each digital sample of said second digital signal s−1(t), four corresponding digital samples with time step (i.e., time distance) T0, thereby generating a corresponding digitally-interpolated signal having the given sampling period T0;        apply, to each set of four digital samples obtained by means of the digital interpolation, digital phase shifts related to the OAM mode −1 with the predefined OAM mode rotation speed (namely, digital phase shifts related to phase values 0, 3π/2, π; and π/2) so as to generate a corresponding set of four phase-shifted digital samples, which corresponding set of four phase-shifted digital samples carries said OAM mode −1 with the predefined OAM mode rotation speed;        digitally filter each set of four phase-shifted digital samples obtained by means of the digital phase shifting so as to output a corresponding set of four filtered digital samples; and        combine the sets of four filtered digital samples obtained by means of the digital filtering into a single filtered signal which represents the space-modulated digital signal sms−1(t).        
The OAM mode generation modules for generating higher-order OAM modes (i.e., with |m|>1) operate, mutatis mutandis, conceptually in the same way as the OAM mode generation modules 110 and 120.
Moreover, again with reference to FIG. 2, the device 100 further comprises:                a combining module 150 operable to combine the first digital signal s0(t) received from the signal generation section 10 and all the space-modulated digital signals smsm(t) generated by the OAM mode generation modules into a corresponding combined digital signal sc(t); and        a transmission filtering module 160, which is operable to digitally filter the combined digital signal sc(t) by means of a predefined transmission filter such that to adjust the signal bandwidth to the bandwidth of transmission radio channel (i.e., the specific radio channel used in transmission) so as to reduce Inter-Symbol Interference (ISI), thereby obtaining a corresponding output digital signal sout(t); wherein the transmission filtering module 160 is coupled with the RF transmission section 1000 to provide the latter with the output digital signal sout(t).        
For example, in case of (free-space) satellite communications on a radio channel having the given frequency bandwidth W, the transmission filter can be a predefined root raised cosine filter adapted to said given frequency bandwidth W.
As for reception side, reference is made to FIG. 3, which shows a functional block diagram of a receiving system (denoted as whole by 2), which is disclosed in WO 2014/016655 A1 and which exploits the aforesaid multidimensional space modulation for receiving radio vortices at frequencies ranging from a few KHz to hundreds of GHz.
In particular, the receiving system 2 comprises:                an RF reception section 2000, which is designed to receive signals at predefined radio frequencies by means of a single antenna (which is not shown in FIG. 3 for the sake of illustration simplicity and which can be also a reflector antenna with a single feed) or an antenna array (which is not shown in FIG. 3 for the sake of illustration simplicity and which can be also a multi-feed reflector antenna), and which is designed to obtain an incoming digital signal uin(t) on the basis of the received signals;        a device 200 for demodulating CAM modes, which is coupled with said RF reception section 2000 to receive the incoming digital signal uin(t) therefrom, and which is designed to process said incoming digital signal uin(t) so as to output useful signals (in FIG. 3 useful signals u0(t), u+1(t), u−1(t), u+N(t) and u−N(t) outputted by the device 200 are shown); and        a signal processing section 20, which is coupled with said device 200 to receive the useful signals outputted by the latter and which is designed to process said useful signals.        
The aforesaid predefined radio frequencies can conveniently range from a few KHz to hundreds of GHz depending on the specific application for which the overall receiving system 2 is designed.
Conveniently, the RF reception section 2000 can be an RF reception section of a receiving system for satellite communications (such as a receiving system of a feeder link Earth station, of a satellite, or of a ground apparatus for satellite communications), of a device for wireless communications (such as LTE-based communications), of a radar system, of a Synthetic Aperture Radar (SAR) system, or of a radio astronomy receiving system.
Accordingly, the signal processing section 20 can conveniently be a signal processing section of a receiving system for satellite communications (such as a receiving system of a feeder link Earth station, of a satellite, or of a ground apparatus for satellite communications), of a device for wireless communications (such as LTE-based communications), of a radar system, of a SAR system, or of a radio astronomy receiving system.
Additionally, FIG. 4 shows in greater detail the device 200 for demodulating OAM modes. In particular, as shown in FIG. 4, the device 200 comprises a reception filtering module 210, which is operable to digitally filter the incoming digital signal uin(t) by means of a predefined reception filter such that to equalize the incoming digital signal uin(t) with respect to reception radio channel (i.e., the specific radio channel used in reception) and, conveniently, also with respect to transmission filter (i.e., the specific filter used in transmission), thereby obtaining a corresponding filtered incoming digital signal uf(t).
For example, in case of (free-space) satellite communications on a radio channel having the given frequency bandwidth W, wherein the transmission filter is a predefined root raised cosine filter adapted to said given frequency bandwidth W, the reception filter can be the complex conjugate of said predefined root raised cosine filter so as to reduce ISI.
Additionally, again with reference to FIG. 4, the device 200 further comprises a digital oversampling module 220 operable to digitally oversample the filtered incoming digital signal uf(t) on the basis of a predefined oversampling period Tover thereby outputting a corresponding set of digital samples.
For example, in case the receiving system 2 is configured to receive the RF signals transmitted by the transmission system 1, the predefined oversampling period Tover can conveniently be equal to T0/Q, wherein T0 is the given sampling period previously introduced in connection with the transmission system 1, and Q denotes an integer higher than one.
Furthermore, again with reference to FIG. 4, the device 200 comprises also a processing module 230 configured to:                provide a linear system of M equations (where M denotes an integer higher than one) relating                    the set of digital samples outputted by the digital oversampling module 220            to X unknown digital values (where X denotes an integer higher than one and lower than M) of useful signals associated, each, with a respective predefined OAM mode m with a predefined OAM mode rotation speed;            wherein said linear system of M equations relates the set of digital samples outputted by the digital oversampling module 220 to the X unknown digital values through                            first predefined parameters related to the predefined OAM modes with the predefined OAM mode rotation speed, and                second predefined parameters related to the predefined reception filter, to the reception radio channel and, conveniently, also to the transmission filter;                                                compute the X digital values by solving the linear system of M equations; and        digitally generate and output the useful signals (for example the useful signals u0(t), u+1(t), u−1(t), u+N(t) and u−N(t) shown in FIG. 4) on the basis of the corresponding digital values computed.        
In this connection, it is important to underline the fact that, in order to extract the useful signals (i.e., in order to solve the linear system of M equations thereby computing the X digital values, and, thence, to generate and output the useful signals), the processing module 230 is conveniently configured to operate as a generalized matched filter which exploits one or more mathematical processing techniques, such as the pseudo-inverse technique.
Moreover, it is also important to underline the fact that the oversampling operation performed by the digital oversampling module 220 allows to increase redundancy of the linear system of M equations (i.e., it allows to obtain a number M of independent equations higher and higher than the number X of the unknown digital values), thereby allowing to find more robust solutions to said linear system of M equations.
Furthermore, the better the characterization of the OAM modes and of the radio channel in the linear system of M equations, the more robust the resolution of said linear system of M equations. Specifically, an increase in the number of first and second predefined parameters used in the linear system of M equations allows to increase redundancy of said linear system of M equations (i.e., it allows to obtain a number M of independent equations higher and higher than the number X of the unknown digital values), thereby allowing to optimize the resolution of, i.e., to find optimum solutions to, said linear system of M equations in terms of energy per bit to noise power spectral density ratio Eb/N0.
In case the receiving system 2 is configured to receive the RF signals transmitted by the transmission system 1, the first predefined parameters are related to the sampling periods T0 and Tm previously introduced in connection with the device 100, and to the digital phase shifts applied by the OAM mode generation modules of the device 100 to the digital samples of the digitally-interpolated signals.
Moreover, again in case the receiving system 2 is configured to receive the RF signals transmitted by the transmission system 1, the useful signals generated and outputted by the processing module 230 (such as the signals u0(t), u+1(t), u−1(t), u+N(t) and u−N(t) shown in FIG. 4) are the digital signals transmitted by said transmission system 1 by means of the plane wave and the several radio vortices (namely the signals s0(t), s+1(t), s−1(t), s+N(t) and s−N(t) shown in FIGS. 1 and 2).
Preferably, the device 100 for generating OAM modes and the device 200 for demodulating OAM modes are implemented by means of Field-Programmable Gate Array (FPGA), Application-Specific Integrated Circuit (ASIC), and Software Defined Radio (SDR) technologies.
Finally, according to a further aspect of WO 2014/016655 A1, an overall radio communication system including both the transmission system 1 and the receiving system 2 is preferably designed to:                monitor interference experienced by the radio vortices transmitted; and,        if the interference experienced by a radio vortex carrying a given digital signal sm(t) by means of a given OAM mode m meets a given interference-related condition (for example, if it exceeds a given interference level),                    start using an OAM mode m* different from the given OAM mode m for transmitting the information stream previously carried by said given digital signal sm(t) by means of said given OAM mode m, and            stop using said given OAM mode m.                        
In case said further aspect of WO 2014/016655 A1 is used for satellite communications, it is possible to mitigate jammer, since said further aspect of WO 2014/016655 A1 allows to reject a jammed OAM mode. Moreover, said further aspect of WO 2014/016655 A1 can be used also in combination with other anti-jamming capabilities of the receiving system.